The arithmetic extensions of a numerical semigroup |
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| Authors: | I Ojeda J C Rosales |
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| Institution: | 1. Departamento de Matemáticas, Universidad de Extremadura, Badajoz, Spain;2. ojedamc@unex.es;4. Departamento de álgebra, Universidad de Granada, Granada, Spain |
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| Abstract: | AbstractIn this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained. |
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| Keywords: | Apery set arithmetic extension extension Frobenius number genus Kunz-coordinates numerical semigroup quotient of a semigroup |
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